So, you have a sample and you really want to show it off. You know you want surface area information, but what kind? How much surface area does it have? Does it have pores? If so, how big are they? Before you are ready to show the world your sample’s true potential, you have to put it to the test! The only question is… which test?

Particle Technology Labs offers many techniques to look at the surface of a sample. Let’s talk about some of the basics of gas physisorption.

## The Big Picture: Gas Physisorption

To set the scene, imagine a solid particle suspended in vacuum. The surface is free of any moisture or atmospheric vapors. When inert gas is introduced to the particle in vacuum, weak interactions occur between the gas and the solid particle surface. It is well known that with decreasing temperature and increasing pressure, the physical adsorption of gas onto the solid increases. This forms the basis for using gas physisorption as an analytical technique.

To perform any surface area analysis using the gas physisorption technique, we need to establish a relationship between quantity of adsorbed gas and relative pressure at constant temperature. Let’s assume we’re performing a static volumetric analysis (Method II in USP <846> or Ph. Eur. 2.9.26). During the analysis, the instrument introduces a known volume of adsorbate gas (e.g. nitrogen or krypton gas) into an evacuated cell containing sample kept at a constant cryogenic temperature (e.g. 77.35 K, the boiling point of LN_{2}). The resulting relative pressure (expressed as P/Po where P is the bulk pressure in the sample cell and Po is the saturation pressure of the adsorptive gas) is then measured. The instrument can determine how much gas has adsorbed onto the particle surface given the amount of gas introduced to the sample cell and the relative pressure in the cell.

The collected data, plotted as volume adsorbed vs. relative pressure, is called an isotherm plot. The plot can span from a zero or partial pressure up to saturation. When increasing the pressure of adsorptive gas, we create the adsorption isotherm. When decreasing the pressure of adsorptive gas, we create the desorption isotherm.

## Closeup: The BET

While the amount of adsorbate gas increases within the sample cell, we can imagine that at some point the particle becomes fully covered in a single layer of gas molecules or atoms. This is referred to as the monolayer. With the Brunauer, Emmett, Teller model (BET), only a portion of the P/Po range is of interest: approx. 0.05 to 0.30 relative pressure. This region is typically where the formation of the monolayer occurs. Let’s take a closer look at this region and the BET model.

By collecting data points in the relative pressure region of interest, the BET theory allows us to predict where the monolayer forms and “count” gas molecules or atoms that have adsorbed onto the particle surface, thereby facilitating the calculation of the sample’s surface area. The total surface area per unit of mass is referred to as the specific surface area and is generally reported in units of m²/g.

PTL offers a 1-point BET, a 3-point BET, and a 5-point BET analysis, but what is the difference? The more BET points included in the measurement, the more resolution the instrument has when determining where the monolayer forms.

A 1-point BET specific surface area analysis is usually recommended for materials for which we have a very good idea where the monolayer forms. A 3-point or 5-point BET specific surface area analysis is useful when we want a little more confidence in finding where the monolayer forms. PTL typically recommends a 3-point BET. You can learn more about specific surface area analyses via Method II, static volumetric physisorption here.

## Zooming Out: The Isotherm

Now that we are familiar with what the BET region offers, what about the rest of the isotherm? Zooming out, we’ll see that evaluating the whole relative pressure range can also provide essential information about a sample.

One may imagine that with increasing relative pressure, multiple layers of adsorbate gas form. Eventually, most if not all pores and cervices in the mesopore range are filled on the particle surface. This lets us go beyond surface area and gives us information about pore size distribution.

In a porous material, smaller pores generally fill with adsorbate sooner than larger pores. We can link relative pressures to pore sizes in an inverse relationship using methods such as those detailed by Barrett, Joyner and Halenda (BJH). By measuring the amount of gas adsorbed at those relative pressure points, the instrument can determine how pores of a specific diameter have been filled. By measuring the desorption of gas, we can glean a little information about the shape of the pores. Learn more information about mesopore measurements here.

PTL offers a 20-point isotherm as well as a 40-point isotherm analysis for porous materials in the mesopore range (analysis covers a wider range of around 17 Å – 3000 Å), using nitrogen gas as the adsorbate only. The analysis consists of either 20 or 40 data points for both adsorption and desorption of nitrogen gas. Both analyses include a reported multi-point BET specific surface area. The 40-point isotherm offers greater resolution for the pore size distribution of a material than the 20-point isotherm.

Pores smaller than 20 Å can be hard to reach, but PTL has advanced instruments capable of probing them. A host of advanced models have been developed to properly account for differing pore shape or size, based on the Density Functional Theory (DFT). Using the advanced instruments and DFT models, PTL can also perform micro-mesopore isothermal analysis for nominal pore dimeters in the range of around 5 Å – 3000 Å. Either nitrogen (at liquid nitrogen temperature) or argon (at liquid argon temperature) may be utilized as the adsorptive gas for this method.

For further discussion on your gas physisorption needs, models that may be utilized for physisorption analysis, or what adsorbate options can be offered, please contact us to speak with one of our surface area specialists.

## That’s a Wrap!

We now have all the information we need to properly show off our star sample. We can determine the sample’s specific surface area by performing a BET analysis, and we can determine a pore size distribution by performing an isotherm analysis. Particle Technology labs can perform these analyses and wrap the results in a comprehensive package to best show off the sample’s potential. Looks like your sample is ready for the big screen!

By Arielle Lopez, Particle Characterization Chemist III.